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Chap002_solutions

# Chap002_solutions - Chapter 2 Descriptive Statistics...

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Chapter 2: Descriptive Statistics CHAPTER 2 Descriptive Statistics 2.1 a. Both halves are mirror images of each other and one peak in the middle, tapering on both ends. b. Two distinct high points. c. Having a long tail to the left. d. Having a long tail to the right. 2.2 a. Stem-and-leaf display: see page 45 Histogram: see page 50 Dot plot: see page 51 b. The class limits are the smallest and largest measurements that can fall in a class, where the class boundaries are set halfway between the class limits to include all measurements. The class midpoint is the middle value in a class. c. Outliers are unusually large or small observations that are well separated from the remaining observations. Outliers are handled differently depending on their cause. 2.3 a. Stem-and-Leaf Display of Profit Margin n = 35 Leaf Unit = 0.10 Frequency Stem 2 1| 1 8 2 2| 2 9 6 3| 1 2 3 6 6 9 4 4| 0 4 7 9 12 5| 0 0 0 2 3 4 8 9 9 9 9 9 3 6| 1 8 9 1 7| 0 1 8| 6 1 9| 2 1 10| 9 1 11| 2 12| 13| 14| 15| 16| 17| 18| 19| 20| 21| 22| 23| 1 24| 0 5

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Chapter 2: Descriptive Statistics Distribution is skewed right. 6
Chapter 2: Descriptive Statistics b. Stem-and-Leaf of Display on Capital n = 35 Leaf Unit = 0.10 Frequency Stem 1 0| 0 1| 2| 3| 1 4| 0 5| 6| 7| 2 8| 3 6 1 9| 2 10| 4 11| 0 2 5 6 3 12| 6 7 8 1 13| 1 3 14| 4 7 7 3 15| 2 4 9 1 16| 5 2 17| 0 6 1 18| 3 3 19| 2 7 8 3 20| 3 6 8 2 21| 1 7 1 22| 8 23| 24| 2 25| 1 7 26| 27| 28| 29| 30| 31| 32| 1 33| 4 Distribution is quite variable, but symmetric with both high and low outliers. c. Profit margins are skewed to the right and less spread out when compared to Return on Capital. 2.4 a. Relatively symmetric, perhaps slight skew to right. b. Symmetric with one high outlier. 7

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Chapter 2: Descriptive Statistics c. Distribution is highly spread out with 1 obvious high outlier. 2.5 a. We have 64 2 6 = and . 128 2 7 = Since 6 2 < n = 65 and 7 2 > n = 65, we use K = 7 classes. Class length = 2 71 . 1 7 12 7 36 48 t measuremen smallest t measuremen largest = = - = - K Class Frequency Relative Frequency Boundaries Midpoint 36 – 37 1 1/65 = .0154 35.5, 37.5 36.5 38 – 39 7 7/65 = .1077 37.5, 39.5 38.5 40 – 41 11 11/65 = .1692 39.5, 41.5 40.5 42 – 43 14 14/65 = .2154 41.5, 43.5 42.5 44 – 45 21 21/65 = .3231 43.5, 45.5 44.5 46 – 47 10 10/65 = .1538 45.5, 47.5 46.5 48 – 49 1 1/65 = .0154 47.5, 49.5 48.5 b. The population of all possible customer satisfaction ratings is slightly skewed with a tail to the left. 8 DotPlot -50% 0% 50% 100% 150% 200% 250% Total Return
Chapter 2: Descriptive Statistics c. The relative frequency histogram would be the same as the frequency histogram in Figure 2.15, except the heights of the rectangles would be the relative frequencies given in the table of part (a). This means the numbers on the vertical axis in Figure 2.15 – 0, 5, 10, 15, 20, 25 – would be divided by 65. Thus, the numbers on the vertical axis would be 0, .077, .154, .231, .308, .385. Alternatively, if we have MINITAB construct a relative frequency histogram by choosing its own classes, we obtain the following: 2.6 a. We have 64 2 6 = and . 128 2 7 = Since 6 2 < n = 100 and 7 2 > n = 100, we use K = 7 classes.

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Chap002_solutions - Chapter 2 Descriptive Statistics...

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